Orthogonality properties of rotated empirical modes

The properties (spatial orthogonality and temporal uncorrelatedness) of ort hogonally rotated empirical modes depend on the normalization of the modes, prior to rotation. It is shown here that these properties also depend on h ow the empirical modes are formulated. The preferred convention is one that allows us to reconstruct the data from the unrotated or rotated modes. Whe n the empirical modes are normalized so that the spatial eigenvectors are u nit length (i.e. empirical orthogonal functions (EOFs)), the rotated modes preserve spatial orthogonality, but are no longer temporally uncorrelated. Relaxing the temporal orthogonality in this way does not prejudice conclusi ons that can be inferred regarding the temporal couplings of the rotated mo des. Copyright (C) 2000 Royal Meteorological Society.